Trang H. Tran, Lam Nguyen, et al.
INFORMS 2022
Let ℂ denote the complex numbers and ℒ denote the ring of complex-valued Laurent polynomial functions on ℂ \ {0}. Furthermore, we denote by ℒR, ℒN the subsets of Laurent polynomials whose restriction to the unit circle is real, nonnegative, respectively. We prove that for any two Laurent polynomials P1, P2 ∈ ℒN, which have no common zeros in ℂ \ {0} there exists a pair of Laurent polynomials Q1, Q2 ∈ ℒN satisfying the equation Q1P1 + Q2P2 = 1. We provide some information about the minimal length Laurent polynomials Q1 and Q2 with these properties and describe an algorithm to compute them. We apply this result to design a conjugate quadrature filter whose zeros contain an arbitrary finite subset Λ ⊂ ℂ \ {0} with the property that for every λ, μ ∈ Λ, λ ≠ μ implies λ ≠ -μ and λ ≠ -1/μ̄.
Trang H. Tran, Lam Nguyen, et al.
INFORMS 2022
Daniel J. Costello Jr., Pierre R. Chevillat, et al.
ISIT 1997
Timothy J. Wiltshire, Joseph P. Kirk, et al.
SPIE Advanced Lithography 1998
M. Shub, B. Weiss
Ergodic Theory and Dynamical Systems